Drag depends on the density
of the air, the square of the velocity, the
air's viscosity and compressibility, the
size and shape of
the body, and the body's inclination to
the flow. In general, the dependence on body shape, inclination, air
viscosity, and compressibility is very complex.
One way to deal with complex dependencies is to characterize the
dependence by a single variable. For drag, this variable is called
the drag coefficient, designated
"Cd." This allows us to collect all the effects, simple and
complex, into a single equation.
The drag equation states that drag D is equal to the
drag coefficient Cd times the density r times half of the
velocity V squared times the reference area A.
D = Cd * A * .5 * r * V^2
For given air
conditions, shape, and inclination of the object, we must determine a
value for Cd to determine drag. Determining the value of the
drag coefficient is more difficult than determining the
lift coefficient because of the multiple
sources of drag. The drag coefficient given above includes form
drag, skin friction drag, wave drag, and induced drag components.
Ram drag is usually included in the net thrust because it depends on
the airflow through the engine. Drag coefficients are almost always
determined
experimentally using a wind
tunnel.
Notice that the area (A) given in the drag equation is given as a
reference area. The drag depends directly on the size
of the body. Since we are dealing with aerodynamic
forces, the dependence can be characterized by some area. But
which area do we choose? If we think of drag as being caused by
friction between the air and the body, a logical choice would be the
total surface area of the body. If we think of drag as being a
resistance to the flow, a more logical choice would be the frontal
area of the body that is perpendicular to the flow direction. And
finally, if we want to compare with the lift coefficient, we should
use the same wing area used to derive the lift coefficient. Since the
drag coefficient is usually determined experimentally by measuring
drag and the area and then performing the division to produce the
coefficient, we are free to use any area that can be easily
measured. If we choose the wing area, rather than the crosssectional
area, the computed coefficient will have a different value. But the
drag is the same, and the coefficients are related by the ratio of
the areas. In practice, drag coefficients are reported based on a
wide variety of object areas. In the report, the aerodynamicist must
specify the area used; when using the data, the reader may have to
convert the drag coefficient using the ratio of the areas.
In the equation given above, the density is designated by
the letter "r." We do not use "d" for density since "d" is often used
to specify distance. In many textbooks on aerodynamics, density is
given by the Greek symbol "rho" (Greek for "r"). The combination of
terms "density times the square of the velocity divided by two" is
called the
dynamic pressure
and appears in Bernoulli's
pressure equation.
You can investigate the various factors that affect drag by using
the FoilSim III Java Applet. (Have fun!) Use
the browser "Back" button to return to this page. If you
want your own copy of FoilSim to
play with, you can download it at
no charge.
You can view a short
movie
of "Orville and Wilbur Wright" discussing the drag force
and how it affected the flight of their aircraft. The movie file can
be saved to your computer and viewed as a Podcast on your podcast player.
Activities:
Guided Tours

Drag Equation:

Factors that Affect Drag:

Rocket Modeler Talk:
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